{"id":"https://openalex.org/W2148381206","doi":"https://doi.org/10.1109/tit.1986.1057210","title":"Complexity of strings in the class of Markov sources","display_name":"Complexity of strings in the class of Markov sources","publication_year":1986,"publication_date":"1986-07-01","ids":{"openalex":"https://openalex.org/W2148381206","doi":"https://doi.org/10.1109/tit.1986.1057210","mag":"2148381206"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1986.1057210","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1986.1057210","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109212464","display_name":"J. Rissanen","orcid":null},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J. Rissanen","raw_affiliation_strings":["IBM ARC, San Jose, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM ARC, San Jose, CA, USA","institution_ids":["https://openalex.org/I1341412227"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109212464"],"corresponding_institution_ids":["https://openalex.org/I1341412227"],"apc_list":null,"apc_paid":null,"fwci":4.121,"has_fulltext":false,"cited_by_count":194,"citation_normalized_percentile":{"value":0.94639003,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"32","issue":"4","first_page":"526","last_page":"532"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6320574879646301},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.6014387607574463},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5810497999191284},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.5546275973320007},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.5290402770042419},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4946410357952118},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.45824193954467773},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4552251100540161},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.43358609080314636},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4251954257488251},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27267658710479736},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2616127133369446},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.2364504635334015}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6320574879646301},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.6014387607574463},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5810497999191284},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.5546275973320007},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.5290402770042419},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4946410357952118},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.45824193954467773},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4552251100540161},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.43358609080314636},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4251954257488251},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27267658710479736},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2616127133369446},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2364504635334015},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1986.1057210","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1986.1057210","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1554869488","https://openalex.org/W1968908999","https://openalex.org/W1969678783","https://openalex.org/W1999120268","https://openalex.org/W2002661259","https://openalex.org/W2005097301","https://openalex.org/W2064533938","https://openalex.org/W2069074906","https://openalex.org/W2077770566","https://openalex.org/W2082967074","https://openalex.org/W2106596127","https://openalex.org/W2119047110","https://openalex.org/W2122962290","https://openalex.org/W2125796582","https://openalex.org/W2128777897","https://openalex.org/W2131024393","https://openalex.org/W2132119275","https://openalex.org/W2154462988","https://openalex.org/W2183235533","https://openalex.org/W4213350211","https://openalex.org/W4214573638"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W1971753667","https://openalex.org/W2052275678","https://openalex.org/W123221615","https://openalex.org/W1969778210","https://openalex.org/W2037817744","https://openalex.org/W2465024128","https://openalex.org/W2106695582","https://openalex.org/W2100732817","https://openalex.org/W2913798541"],"abstract_inverted_index":{"Shannon's":[0,66],"self-information":[1],"of":[2,14,58,74],"a":[3,41,50,71,77],"string":[4],"is":[5,26,36,80],"generalized":[6],"to":[7,11],"its":[8],"complexity":[9,48],"relative":[10],"the":[12,23,46,55,84],"class":[13],"finite-state-machine":[15],"(FSM)":[16],"defined":[17],"sources.":[18],"Unlike":[19],"an":[20],"earlier":[21],"generalization,":[22],"new":[24],"one":[25],"valid":[27],"for":[28,54,82],"both":[29],"short":[30],"and":[31],"long":[32],"strings.":[33],"The":[34],"definition":[35],"justified":[37],"in":[38],"part":[39],"by":[40],"theorem":[42],"stating":[43],"that,":[44],"asymptotically,":[45],"mean":[47,56],"provides":[49],"tight":[51],"lower":[52],"bound":[53],"length":[57],"all":[59],"so-called":[60],"regular":[61],"codes.":[62],"This":[63],"also":[64],"generalizes":[65],"noiseless":[67],"coding":[68],"theorem.":[69],"For":[70],"large":[72],"subclass":[73],"FSM":[75],"sources":[76],"simple":[78],"algorithm":[79],"described":[81],"computing":[83],"complexity.":[85]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}